1,1

The terms in the sequence are floor(2^b), floor(2^2^b), floor(2^2^2^b), ..., where b is approximately 1.2516475977905.

The existence of b is a consequence of Bertrand's postulate.

a(5) is much larger than the largest known prime, which is currently only 2^32582657-1. - T. D. Noe (noe(AT)sspectra.com), Oct 18 2007

This sequence is of course not computed from b; rather b is more precisely computed by determining the next term in the sequence.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Exercise 4.19.

The smallest prime after 2^5 = 32 is 37, so a(5) = 37.

Cf. A079614 (Bertrand's constant).

Sequence in context: A084436 A053609 A036780 this_sequence A135378 A077398 A067083

Adjacent sequences: A051498 A051499 A051500 this_sequence A051502 A051503 A051504

nonn

Jud McCranie (j.mccranie(AT)comcast.net)

Although the exact value of the next term is not known, it has 41373247571 digits.

Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 10 2009